Commute Time Embedding Research Articles

Efficient large scale commute time embedding

Commute time embedding involves computing eigenfunctions of the graph Laplacian matrix. Spectral decomposition requires computational burden proportional to O(n3), which may not be suitable for large scale dataset. This paper proposes computationally efficient commute time embedding by applying Nyström method to the normalized graph Laplacian. The performance of the proposed algorithms is analysed by checking the embedding results on a patch graph.

파형 신호에 대한 다양체 임베딩의 위상학적 불변항의 분석

This paper raises a question of whether a simple periodic phenomenon is associated with the topology and provides the convincing answers to it. A variety of music instrumental sound signals are used to prove our assertion, which are embedded in Euclidean space to analyze their topologies by computing the homology groups. A commute time embedding is employed to transform segments of waveforms into the corresponding geometries, which is implemented by organizing patches according to the graph-based metric. It is shown that commute time embedding generates the intrinsic topological complexities although their geometries are varied according to the spectrums of the signals. This paper employs a persistent homology to determine the topological invariants of the simplicial complexes constructed by randomly sampling the commute time embedding of the waveforms, and discusses their applications.

FctClus: A Fast Clustering Algorithm for Heterogeneous Information Networks.

It is important to cluster heterogeneous information networks. A fast clustering algorithm based on an approximate commute time embedding for heterogeneous information networks with a star network schema is proposed in this paper by utilizing the sparsity of heterogeneous information networks. First, a heterogeneous information network is transformed into multiple compatible bipartite graphs from the compatible point of view. Second, the approximate commute time embedding of each bipartite graph is computed using random mapping and a linear time solver. All of the indicator subsets in each embedding simultaneously determine the target dataset. Finally, a general model is formulated by these indicator subsets, and a fast algorithm is derived by simultaneously clustering all of the indicator subsets using the sum of the weighted distances for all indicators for an identical target object. The proposed fast algorithm, FctClus, is shown to be efficient and generalizable and exhibits high clustering accuracy and fast computation speed based on a theoretic analysis and experimental verification.